Practical deployments of MR LRCs typically have a small number of local groups (say \(g=2,3,4\) ) and a small number of local parities per local group (say \(a=1,2\) ) [1]}. Moreover, field size is the most important determinant of encoding and decoding efficiency of MR LRCs [1]}, since encoding and decoding requires several finite field operations. Therefore constructions of MR LRCs over small fields in this regime are important in practice.
